Speaker: Andrew Neitzke, Yale University

Location: Harvard University Science Center Hall D & via Zoom webinar

Dates: October 16 & 17, 2024

Time: 4:00 pm

Wednesday, Oct. 16, 2024

Title: Abelianization in analysis of ODEs

Abstract: I will describe the exact WKB method for asymptotic analysis of families of ODEs in one variable, and its interpretation as a kind of abelianization procedure, which replaces GL(N)-connections over a Riemann surface by GL(1)-connections over an N-fold branched cover. This abelianization procedure connects exact WKB to various subjects in geometry (cluster algebras, moduli of Higgs bundles, enumerative geometry). One application is a conjectural description of Hitchin’s hyperkahler metric on the moduli of Higgs bundles; I will review some recent progress on these conjectures.

Thursday, Oct. 17, 2024

Title: Abelianization in quantum topology

Abstract: I will describe new applications of abelianization to various related subjects: perturbative Chern-Simons invariants, skein algebras, and conformal blocks. The aim is to explain how abelianization gives a unifying perspective on constructions familiar in each of these subjects (e.g. dilogarithmic formulas for Chern-Simons invariants, vertex models for computing quantum invariants of links, and iterated-fusion constructions of conformal blocks for the Virasoro algebra), and also suggests various extensions, which are just beginning to be explored.

Raoul Bott (9/24/1923 – 12/20/2005) is known for the Bott periodicity theorem, the Morse–Bott functions, and the Borel–Bott–Weil theorem.